Aside from the MMSE and MMDDT criteria some works consider the direct optimization of symbol error probability (SEP) for precoding design e.g. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. While the studies from [1]}, [2]}, [3]}, [4]} mainly focus on QAM signaling with 1-bit data converters, [5]} considers M-PSK modulation shows that by using the MMDDT design one can minimize an upper bound on the SEP. Another relevant result was achieved in [6]} where an analytical formula for the SEP using QPSK data modulation is derived and, based on it, a discrete optimization problem is formulated.
